Fractal Worlds, a text by Michael Frame and Amelia Urry
Mandelbrot's 2010 TED talk
Frame's 2013 TEDxYale talk
Fractal geometry coursepage
Java Software
Panorama of Uses
1. Introduction to Fractals
1A. Self-Similarity
1B. More Examples of Self-Similarity
1C. Initiators and Generators
1D. Geometry of Plane Transformations
1E. Iterated Function Systems
1F. Inverse Problems
1G. Random IFS
1H. Driven IFS
1I. Architecture
2. Natural Fractals and Dimensions
2A. Ineffective Ways to Measure
2B. Box-Counting Dimension
2C. Similarity Dimension
2D. The Moran Formula
2E. Other Dimensions
2F. Area-Perim
2G. Dim Algebra
2H. Natural Fractals
2I. Manufactured Fractals
3. The Mandelbrot Set and Julia Sets
3A. Complex Iteration
3B. Julia Sets
3C. The Mandelbrot Set
3D. Combinatorics of the Mandelbrot Set
3E. The Boundary of the Mandelbrot Set
3F. Scalings in the Mandelbrot Set
3G. Complex Newton's Method
3H. Universality of the Mandelbrot Set
3I. Mandelbrot Monk
3J. Fractals in Literature
3K. Fractals in Art
4. Cellular Automata and Fractal Evolution
4A. Self-Replicating Machines
4B.Cellular Automata Basics
4C. Cellular Automata Patterns
4D. Genetic Algorithms
4E. Fractal Fitness Landscapes
4F. 1/f Noise
4G. Music, including 1/f
4H. Fractal History
4I. Video Feedback
4J. Leopard Spots
4K. Neural Nets
4L. Artificial Life
5. Random Fractals and the Stock Market
5A. Self-Similar Distributions
5B. Brownian Motion
5C. Fractional Brownian Motion
5D. Levy Flights
5E. Diffusion-Limited Aggregation
5F. Percolation
5G. Bacterial Growth
5H. Galaxy Distributions
5I. Internet Traffic
5J. Random Fractal Cartoons
5K. Stock Market Surrogates
6. Chaos
6A. Doubling
6B. Introduction to Chaos
6C. Test Functions
6D1. Graphical Iteration
6D2. Time Series
6D3. Histograms
6D4. Bifurcation Diagrams
6D5. Return Map
6D6. Driven IFS
6D7. Kelly Plot
6E. Fixed Points
6F. Cycles
6G. Period-doubling Bifurcation
6H. Chaos Definition
6I. Dust in the Tent Map
6J. Tent and Logistic Bifurcation Diagrams
6K. Tangent Bifurcation
6L. Intermittency
6M. Discontinuous Bifurcations
6N. Scaling
6O. Universality
6P. Renormalization
6Q. Driven IFS
6R. Kelly Plot
6S. Control of Chaos
6T. Synchronization of Chaotic Processes
7. Multifractals
7A. Unequal Probabilities
7B. Histograms
7C. Another Example
7D. Local Dimensions
7E. Multifractals from IFS
7F. f(a) curves
7G. f(a) from financial data
8. Fractal Trees
8A. Definitions
8B. Self-Contact
8C. Dimension
8D. Animationss
9. Circle Inversions
9A. Inversion properties
9B. Limit Sets
9C. Overlapping circles
9D. Animations
9E. Mandelbrot's Algorithm
9F. Dimensions
9G. Restricted Limit Sets
9H. Driven IFS
Lesson Plans
Mathematica Notebooks
School Work